Abstract
Given two semi-regular matrices \( \mathfrak{M} \) and \( \mathfrak{M}' \) and two open subsets Ω and Ω′ [resp. two compact subsetsK andK′] of \( \mathbb{R}^r \) and \( \mathbb{R}^s \) respectively, we introduce the spaces \( \mathcal{E}_{(\mathfrak{M} \times \mathfrak{M}')} \) (Ω × Ω′) and \( \mathcal{D}_{(\mathfrak{M} \times \mathfrak{M}')} \) (Ω × Ω′) [resp. \( \mathcal{D}_{(\mathfrak{M} \times \mathfrak{M}')} \) (K ×K′)]. In this paper we study their locally convex properties and the structure of their elements. This leads in [10] to tensor product representations of these spaces and to some kernel theorems.
Resumen
Dadas dos matrices semi-regulares \( \mathfrak{M} \) y \( \mathfrak{M}' \) y dos subconjuntos abiertos Ω y Ω′ [respectivamente dos subconjuntos compactosK yK⊥] de \( \mathbb{R}^r \) y \( \mathbb{R}^s \) respectivamente, introducimos los espacios \( \mathcal{E}_{(\mathfrak{M} \times \mathfrak{M}')} \) (Ω × Ω′) y \( \mathcal{D}_{(\mathfrak{M} \times \mathfrak{M}')} \) (Ω × Ω′) [respectivamente \( \mathcal{D}_{(\mathfrak{M} \times \mathfrak{M}')} \) (K ×K′)]. En este artículo estudiamos sus propiedades localmente convexas y la estructura de sus elementos, lo que nos ha permitido en [10] obtener representaciones de estos espacios en productos tensoriales y algunos teoremas de núcleos.
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Schmets, J., Valdivia, M. Mixed intersections of non quasi-analytic classes. Rev. R. Acad. Cien. Serie A. Mat. 102, 211–220 (2008). https://doi.org/10.1007/BF03191822
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DOI: https://doi.org/10.1007/BF03191822